On/off determines your black level for a given white level - so if you have 12ft lamberts at full white, and 2000:1 on/off CR (average DLP), your black level is 0.006ft lamberts which is the best black you can ever display (such as a full blackout or night scene). If your on/off CR is 8000:1 like a CRT calibrated for good shadow detail, then the black level will be 4 times blacker at 0.0015ft lamberts, so on/off is very important for black level. You can dim the lesser capable CR machine down using a filter, but then you end up with very good blacks and a very dim image. It's quite possible (and probable) that a scene may require the full range of the display, such as with a full moon in a night scene, or a space scene with a brightly lit space ship interior in view.
Contrast range is important for rendering shadow detail. If the black level is poor and the CR is low, you will be losing detail where shadows should be visible. This is very obvious with some older low on/off capable LCDs which look very grey when displaying black and do not display shadow detail very well. They can look very 'flat' because of it.
ANSI capability is important for showing bright and shadow detail in the same frame at the same time. CRTS have low ANSI capability because of their lenses (bright parts contaminate the black parts due to lens light scatter), but have higher on/off CR and still produce what many consider to be the best displays available.
Even if the source contains a range of just 1000:1, the higher CR machine will produce the better blacks with the same white level, so to say higher CR is useless isn't really true.
Gary.